A Cylindrical Void Growth Model in Visco-Plastic Materials

Abstract

Based on the general macroscopic potential theory, a method to find macroscopic plastic potential and the corresponding constitutive relation is developed for visco-plastic materials containing cylindrical voids. The constitutive relation of the matrix has a generalized overstress form. A comparison of the exact macroscopic potential with its upper bound is made. The numerical results show little difference between the upper bound potential and the exact one. The macroscopic constitutive relation is investigated under triaxial loading conditions. When the strain rate sensitive parameter tends to zero, Gurson's model (1977) is retrieved. When the loading condition is axisymmetric, the present result reverts to Licht and Suquet's result (1988). When the matrix becomes infinite, the result of Budiansky et al. (1982) is obtained. Finally, the macroscopic constitutive relation and the corresponding dynamic loading surface are investigated for the case of axisymmetric load. An approximate analytical expression of the dynamic loading surface is suggested through analysis and numerical fitting.KEY WORDS: plastic potential, visco-plastic material, cylindrical void growth, dynamic loading surface.

Meshfree Simulations of Ductile Crack Propagations

“…First, there have been regularized versions of the Gurson model proposed (e.g. Pan and Huang [1994]); however, the digital version of a regularized Gurson model is still developing. The GTN model used in this simulation is the standard version used in numerical computations, which has been extensively used in research to study ductile failures; recent works include: Pardoen and Hutchinson [2000], Benzerga [2002], Becker [2002], and Besson and Guillemer-Neel [2003].…”

Experimental investigation into plastic damage of microvoids with interaction

“…where the coefficient am,,, axe = a2Sin (m~rb=/p=o) sin (nlrby/p~o) (2) am,n m~rbz/p=o nlrb~/pvo and fx0, f~0 are the initial frequencies of the grid pattern without any deformation, related to the grid pitches Px0 and py0 given by…”

“…In the last decades, many models have been presented to analyze the void nucleation, growth and coalescence, such as that by Gurson [1] for the voids in perfect rigid-plastic materials; that by Pan and Huang [2] for the voids in visco-plastic materials, and many others as reviewed by Curran, Seaman and Shockey [3] for the voids involved in the materials under dynamic loading conditions, etc. Experimental work has been essential to study the mechanism of void growth and coalescence, and to establish the failure model and the constitutive relation of the materials containing microvoids.…”